Why start at x, y, z - User contributions [en-gb]

Talk:Modular equivalence

2021-07-02T18:28:24Z

RJBoland: Alternate Mod Notation

[[Category:Unpleasantness]]

Mod notation can be bulky and counter-intuitive. Here is an alternate mod notation that simply removes the middle line from the equivalence sign, places the modulus inside and drops the now moot 'mod'.

The following macros are defined for the Latex that follows and the second graphic shows the result:

[[File:Modmacros.png|left|alt=Alternate mod Latex macros|Alternate mod Latex macros]]

Examples:
In lieu of $x\equiv y \mod{z}$, we have $x\bm{z}y$

Rather than take both sides $\mod{m}$, we would take both sides $\bm{m}$

Taking all $m\bm{7}1\in \mathbb{Z}_{+}$ gives $\{1,8,15,\dots\}$

A non-equivalence can be written $9\bmn{4}3$

It can be chained ala $27\bm{11}5\bm{3}2$

and even be adapted to carry quotient information as in $77\bmq{13}{5}12$.

Here's how that looks when rendered:

[[File:Modexamples.png|left|alt=Alternate mod notation as rendered in Latex|Alternate mod notation as rendered in Latex]]

Talk:Modular equivalence

2021-07-02T18:24:36Z

RJBoland:

[[Category:Unpleasantness]]

Mod notation can be bulky and counter-intuitive. Here is an alternate mod notation that simply removes the middle line from the equivalence sign, places the modulus inside and drops the now moot 'mod'.

The following macros are defined for the Latex that follows and the second graphic shows the result:

[[File:Modmacros.png|left|alt=Alternate mod Latex macros|Alternate mod Latex macros]]

Examples:
In lieu of $x\equiv y \mod{z}$, we have $x\bm{z}y$
Rather than take both sides $\mod{m}$, we would take both sides $\bm{m}$
Taking all $m\bm{7}1\in \mathbb{Z}_{+}$ gives $\{1,8,15,\dots\}$
A non-equivalence can be written $9\bmn{4}3$
It can be chained ala $27\bm{11}5\bm{3}2$
and even be adapted to carry quotient information as in $77\bmq{13}{5}12$.

Here's how that looks when rendered:

[[File:Modexamples.png|left|alt=Alternate mod notation as rendered in Latex|Alternate mod notation as rendered in Latex]]

Talk:Modular equivalence

2021-07-02T18:23:57Z

RJBoland: Alternate Mod Notation

[[Category:Unpleasantness]]

Mod notation can be bulky and counter-intuitive. Here is an alternate mod notation that simply removes the middle line from the equivalence sign, places the modulus inside and drops the now moot 'mod'.

The following macros are defined for the Latex that follows and the second graphic shows the result:

[[File:Modmacros.png|left|alt=Alternate mod Latex macros|Alternate mod Latex macros]]

Examples:
In lieu of $x\equiv y \mod{z}$, we have $x\bm{z}y$
Rather than take both sides $\mod{m}$, we would take both sides $\bm{m}$
Taking all $m\bm{7}1\in \mathbb{Z}_{+}$ gives $\{1,8,15,\dots\}$
A non-equivalence can be written $9\bmn{4}3$
It can be chained ala $27\bm{11}5\bm{3}2$
and even be adapted to carry quotient information as in $77\bmq{13}{5}12$.

Here's how that looks when rendered:

[[File:Modexamples.png|left|alt=Alternate mod notation as rendered in Latex|Alternate mod notation as rendered in Latex]]

This notation is more compact, intuitive, flexible, prettier, puts the modulus in the middle where it belongs and there is no dead mathematician named Mod being dishonored and forgotten and even if there were, he or she should be.

File:Modexamples.png

2021-07-02T18:21:28Z

RJBoland:

Alternate mod examples rendered in Latex

Talk:Modular equivalence

2021-07-02T18:14:38Z

RJBoland: Alternate Mod Notation

[[Category:Unpleasantness]]

Alternate Mod Notation

Modular equivalence

2021-07-02T17:22:16Z

RJBoland: Blanked the page

Category:Unpleasantness

2021-07-02T17:20:58Z

RJBoland: Blanked the page

Category:Unpleasantness

2021-07-02T17:19:20Z

RJBoland: Mod Notation

[[Category:Unpleasantness]]

Category:Unpleasantness

2021-07-02T17:15:45Z

RJBoland: Blanked the page

Modular equivalence

2021-07-02T17:15:08Z

RJBoland: Mod Notation

Mod Notation Test

Category:Unpleasantness

2021-07-02T17:14:15Z

RJBoland: Mod Notation

[[Mod Notation]]

test

Category:Unpleasantness

2021-07-02T17:06:28Z

RJBoland:

Mod notation can be bulky and counter-intuitive. Here is a mod notation that simply removes the middle line from the equivalence sign, places the modulus inside and drops the now moot 'mod'.

The following 3 Latex macros are used to produce the alternate notation suggested below:

[[File:modmacros.png|Alternate mod notation macros]]

Examples:

In lieu of $x\equiv y \mod{z}$, we have $x\bm{z}y$

Rather than take both sides $\mod{m}$, we would take both sides $\bm{m}$

Taking all $m\bm{7}1\in \mathbb{Z}_{+}$ gives $\{1,8,15,\dots\}$

A non-equivalence can be written $9\bmn{4}3$

It can be chained ala $27\bm{11}5\bm{3}2$

and even be adapted to carry quotient information as in $77\bmq{13}{5}12$.

It is better because it is more compact, intuitive, flexible, prettier, puts the modulus in the middle where it belongs and there is no dead mathematician named Mod being dishonored and forgotten and even if there were, he or she should be.

Category:Unpleasantness

2021-07-02T17:00:32Z

RJBoland: Mod Notation

Mod notation can be bulky and counter-intuitive. Here is a mod notation that simply removes the middle line from the equivalence sign, places the modulus inside and drops the now moot 'mod'.

Examples:

In lieu of $x\equiv y \mod{z}$, we have $x\bm{z}y$

Rather than take both sides $\mod{m}$, we would take both sides $\bm{m}$

Taking all $m\bm{7}1\in \mathbb{Z}_{+}$ gives $\{1,8,15,\dots\}$

A non-equivalence can be written $9\bmn{4}3$

It can be chained ala $27\bm{11}5\bm{3}2$

and even be adapted to carry quotient information as in $77\bmq{13}{5}12$.

It is better because it is more compact, intuitive, flexible, prettier, puts the modulus in the middle where it belongs and there is no dead mathematician named Mod being dishonored and forgotten and even if there were, he or she should be.

File:Modmacros.png

2021-07-02T16:27:16Z

RJBoland:

Latex Macros for better mod notation